"What if the convicted man's family shares his values"

We don't (officially) convict the family, of an individuals crime. If we did, we'd be convicting all family members of whatever crime their relations commit. Be a bummer for lots of people (including the nice family members of all kinds of wealthy and well connected people) if they were to be tarred with the same brush as those who have done terrible things. Of course, so many well connected people, get away with it in the first place, so maybe that wouldn't be such a big problem.